Why isn't my proportion working? (percentages of inputs, per volume)

[hermesbardon]

I'm 33, and I've long used proportions--kids, I promise you, you WILL use math throughout your life.

I set up what I thought was a simple proportion, but it's not working, can anyone explain why?

12oz beer. Xoz vodka
------------=-----------
5% alcohol 40% alcohol

12. X
----=------
.05. .40

The math doesn't get me to about 1.5oz.

What am I doing wrong?

Thank you!!!

 

[tkhunny]

12 / 0.05 = 240

12 * 0.05 = 0.06

Check your Units - ALWAYS. It's not always a division problem.

 

[JeffM]

I agree with tkhunny, but I find his explanation overly condensed.

\(\displaystyle x = \text { oz of vodka.}\)

\(\displaystyle 0.05 * 12 = 0.6 \text { oz alcohol in 12 oz of 5% beer.}\)

\(\displaystyle 0.4x = 0.6 \implies x = \dfrac{0.6}{0.4} = 1.5 \text { oz of 40% vodka.}\)

Percentages already are proportions, and 5% is not equal to 40%. It is easy to go wrong when you start using proportions in proportions.

\(\displaystyle 40\% = \dfrac{0.6}{1.5} \ne \dfrac{0.6}{12} = 5\%.\)

Now where tkhunny is absolutely correct is that dimensional analysis will keep you straight on many, many problems.